Alexey V. Chernov

A closer look at adaptive regret

For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t1, t2] is the loss of the algorithm minus the loss of the best expert over that interval. Adaptive regret measures how well the algorithm approximates the best expert locally, and so is different from, although closely related to, both the classical regret, measured over an initial time interval [1, t], and the tracking regret, where the algorithm is compared to a good sequence of experts over [1, t]. We investigate two existing intuitive methods for deriving algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. We provide a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds follow. We prove that Fixed Share is optimal for adaptive regret: the worst-case adaptive regret of any algorithm is at least that of an instance of Fixed Share.

Prediction with expert advice under discounted loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting and the impact of old losses can gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression, propose a new variant of exponentially weighted average algorithm, and prove bounds on the cumulative discounted loss.

On-Line Probability, Complexity and Randomness

Classical probability theory considers probability distributions that assign probabilities to all events (at least in the finite case). However, there are natural situations where only part of the process is controlled by some probability distribution while for the other part we know only the set of possibilities without any probabilities assigned. We adapt the notions of algorithmic information theory (complexity, algorithmic randomness, martingales, a priori probability) to this framework and show that many classical results are still valid.

Supermartingales in Prediction with Expert Advice

This paper compares two methods of prediction with expert advice, the Aggregating Algorithm and the Defensive Forecasting, in two different settings. The first setting is traditional, with a countable number of experts and a finite number of outcomes. Surprisingly, these two methods of fundamentally different origin lead to identical procedures. In the second setting the experts can give advice conditional on the learners future decision. Both methods can be used in the new setting and give the same performance guarantees as in the traditional setting. However, whereas defensive forecasting can be applied directly, the AA requires substantial modifications.

An Investigation on Online Versus Batch Learning in Predicting User Behaviour

An investigation on how to produce a fast and accurate prediction of user behaviour on the Web is conducted. First, the problem of predicting user behaviour as a classification task is formulated and then the main problems of such real-time predictions are specified: the accuracy and time complexity of the prediction. Second, a method for comparison of online and batch (offline) algorithms used for user behaviour prediction is proposed. Last, the performance of these algorithms using the data from a popular question and answer platform, Stack Overflow, is empirically explored. It is demonstrated that a simple online learning algorithm outperforms state-of-the-art batch algorithms and performs as well as a deep learning algorithm, Deep Belief Networks. The proposed method for comparison of online and offline algorithms as well as the provided experimental evidence can be used for choosing a machine learning set-up for predicting user behaviour on the Web in scenarios where the accuracy and the time performance are of main concern.

Complexity of Sets Obtained as Values of Propositional Formulas

Interpretation of logical connectives as operations on sets of binary strings is considered; the complexity of a set is defined as the minimum of Kolmogorov complexities of its elements. It is readily seen that the complexity of a set obtained by the application of logical operations does not exceed the complexity of the conjunction of their arguments (up to an additive constant). In this paper, it is shown that the complexity of a set obtained by a formula Φ is small (bounded by a constant) if Φ is deducible in the logic of weak excluded middle, and attains the specified upper bound otherwise.

Environmental and human impacts on sediment transport of the largest Asian rivers of Russia and China

The paper deals with comparative summary of sediment loads and particulate trace metals (V, Cr, Co, Cu, Zn, Cd, Pb) transport in the largest Asian rivers of Russia and China. Environmental conditions and human interventions in the selected catchments (Lena, Ob, Enisey, Selenga, Kolyma, Amur, Yellow, Yangtze, Pearl) are analyzed with respect to the rate and composition of suspended sediment loads. The paper presents calculations of sediment load changes at the downstream sections of the rivers and new database of the chemical composition of suspended matter which involves all recent studies of the last decade for the sediment geochemistry. The results indicate that fluvial system and its human modifications are the most significant drivers of sediment load. Fluvial erosion in the unconfined channels exerts a significant control on the sediment load changes due to observed permafrost melting. We concluded that construction of reservoirs has the most important influence on land–ocean sediment fluxes in the largest rivers of Asia but plays relatively weak role in heavy metal composition in suspended particulate matter (SPM) due to lowest sedimentation rates of the fine clay particles, which are mostly enriched with heavy metals. The paper also presents novel mapping approaches related to cartographic recognition of the fluvial system and its human modification and sediment transfer processes in the largest Asian rivers of Russia and China, linked with a specific legend. Finally, analysis of uncertainties associated with estimating the SPM composition in the rivers was done with respect to spatial and temporal variability. It was shown that the main error occurs due to incorporation of data only from particular hydrological seasons which usually ignore high flood conditions.

First data on the Middle to Late Holocene dynamics of vegetation in the Upper Kama region

A detailed palynological record and the results of radiocarbon dating of sediments from the Dedyukhinskii floodplain massif in the vicinity of Lake Chashkinskoe (the Upper Kama region; 59°23′ N, 56°34.5′ E) have been used to reconstruct basic stages in the Middle to Late Holocene dynamics of vegetation. The results show that in the Atlantic period broadleaf tree species played a secondary role in forest formations of taiga and subtaiga types. Broadleaf–conifer forests became dominant in the Subboreal period, with fir widely spreading in the forests during its second half. During the Subatlantic period, forest formations acquired their recent taiga character.

Prefix-Like complexities and computability in the limit

Computability in the limit represents the non-plus-ultra of constructive describability. It is well known that the limit computable functions on naturals are exactly those computable with the oracle for the halting problem. However, prefix (Kolmogorov) complexities defined with respect to these two models may differ. We introduce and compare several natural variations of prefix complexity definitions based on generalized Turing machines embodying the idea of limit computability, as well as complexities based on oracle machines, for both finite and infinite sequences.